Poker Variance Calculator

This variance calculator and simulator for poker is handy and easy to use. Just enter your winrate, standard deviation and the amount of hands to simulate. You'll most certainly get insightful results.Read below how to use this simulator.

20 samples and confidence intervals

Hit "Calculate"!

EV, confidence intervals and samples in BB, Best / Worst: Best and worst run out of 1000 trials

Variance in numbers

Detailed sample with downswings

Hands:
1.0 Million hands

Winnings in BB on right axis, current downswing in BB on left axis. Depending on the number of hands displayed, the extent and number of downswings may be underrepresented due to the resolution of the graph.

Downswings in numbers

This section will explain how the calculator works and what the numbers and charts mean.

Enter the data

Poker Variance Calculator Settings

Hop over to the Variance Calculator page and enter your winrate, standard deviation and the number of hands you want to simulate. You can ignore the field observed winrate, we'll get to its purpose later. Once you have entered the data, hit Calculate and the let the Calculator do its magic.

20 samples

Poker Variance Simulator 20 samples

The first thing the Variance Calculator does, is to run 20 samples over the amount of hands, winrate and standard deviation specified.

It'll also calculate the expected winnings over the amount of hands. This number will appear as a rather boring straight and black line in the graph.

Thirdly the calculator displays the 70% and 95% confidence intervals as light and dark green curves. What you need to know about them is that at any given time your winnings will be within these intervals with a probability of 70% and 95% respectively. They basically show, how much variance you should expect to see.

Variance in numbers

Below the first chart the Variance Calculator compiles a neat list of additional information:

EV: win rate entered above

Standard deviation: standard deviation entered above

Hands: number of hands entered above

Expected winnings: estimated winnings over the simulated amount of hands

Standard deviation after X hands: This number shows by how much your actual results will differ from the expected results on average. The first number shows the absolute value, the second translates this number into BB/100, showing the impact on your winrate.

70% confidence interval: Your actual results over the simulated amount of hands will be within this interval 70% of the time. The first interval shows absolute numbers, the second translates those into BB/100, showing the 70% confidence interval for your winrate.

95% confidence interval: Same as the above with 95% certainty. Meaning: 19 out 20 times your actual winnings will be within this interval.

Probability of loss after X hands: probability that you will experience negative winnings (meaning: losses) over the amount of hands

Probability of running at or above observed win rate …: If you entered an observed winrate, this number will show you the probability that you will experience a run at or above this winrate over the amount of hands.

Probability of running below observed win rate …: Same as above – probability that you will experience a run below the observed winrate over the amount of hands.

Minimum bankroll for less than 5% risk of ruin: the bankroll needed to have a risk of ruin of less than 5%

Detailed sample with downswings

Poker Downswing Simulator

This chart simulates a single run over 100 thousand up to 10 million hands with the winrate and standard deviation entered above. You can choose how many hands to simulate by moving the slider.

Apart from showing a single sample, this graph also shows some insightful information about downswings.

The red area shows for any given point, how much the sample is currently away from its previous peak, meaning it tracks downswings.

This chart uses two vertical axes. While the sample winnings have their scale on the right axis, the downswing tracker has its scale on the left axis.

In this example the simulated player ended up with winnings over 25,000 big blinds after 2.5 million hands but had to deal with a nasty downswing of almost 10,000 big blinds between hand 1.2 million and hand 2 million.

Downswings in numbers

The last section of the Variance Calculator sheds some more light on potential downswings. Therefor 100 million hands are simulated and all downswings over this simulation are tracked.The first table shows the extents of downswings. It shows how often the simulated player was stuck in a downswing of at least X big blinds. For example (1000+ BB – 31.77%) means the player was in the middle of a downswing of at least 1,000 big blinds 31.77 percent of the time.The second table shows how long downswings last on average. For example (50000+ Hands – 15.81%) means the simulated player was in a downswing over at least 50,000 hands 15.81 percent of the time.
For the purpose of these calculations a downswing is defined as any period where the current total winnings are below the maximum previous total winnings. Meaning, by this definition a downswing is not over until the player has fully recovered its losses.
In general these simulations underestimate the extent of downswings, but the numbers should still give you a decent idea of the vastness of downswings you should expect.

I noticed that the 20 random graphs in cg variance simulator almost always have one graph that is outside of the 2 std deviation line..
20 graphs, 1 should be over that 95% line sometimes right.. but not always.

How are the graphs calculated? just a std deviation calculation or something else?

To get it slightly more in line with a hyper stt bubble environment I filtered “Stack” < 25BB and only co/btn/sb/bb and my numbers were 3.5K hands @ 75.19 EV (69.92) with SD 115.26 – both my actual rates are well within the 70% confidence intervals.

The 100% confidence interval would be the range all the way from losing every hand to winning every hand, which is as wide as it could get – you can be 100% confident that a trial will net something in that range.

An expected 5% of trials will net outside the bounds of the 95% interval; an expected 30% of trials will net outside the bounds of the 70% interval.

I’m trying to figure out a fair cut for a cash game deal so i did this:

i added up all numbers from the 20 samples end results divided that number by 20 to get the average result…which should be round about the EV but its not even close…its always way less…i did that a couple of times even with samples that were looking good and its always way less than the EV…

Am confused if the BB is big bet or big blind. I would assume it is big bet. But I look at this noah SD artical which would sugest a +/-8 Big Blinds for 50Kh, but according to this calculator it is about +/- 8 Big Bets over 50Kh(using an SD of 95)

@wiZ
The numbers, u refer to only make sense if you entered an observed winrate. If your ture winrate is 2.5bb/100 then it is very unlikely you will run 10bb/100 (which is the observed winrate) over 100000 hands. if you chose the same winrates for the true and the observed winrate, then you will see, that it is 50%.

can anyone tell me why it is statistically more likely to run BELOW EV than it is to run ABOVE/EQUAL TO EV??? Wow if someone could explain this to me I would be very grateful, right now I do not understand why it would be MORE likely to run below EV than at/above EV? Especially since, even though I am a small winner in my games, I am perpetually running below EV and my actual winnings should be much higher than they currently are. Thank you.

Can anybody please explain to me why (if I interpreted the stats below correctly) it is more likely to run below EV (93,1)% than above/equal to EV (6,9%)over 100k hands? I always see people on the forums : ) say it is as likely to run below EV or above EV but this says otherwise. Help explaining this would be greatly appreciated.

Look, Andrey, you may start playing with your Min BR of 14979 with 5% risk of ruin at a certain distance, but the more you play there is the bigger chance to have a downswing of 15k bb. You see, those tables were simulated at the distance over 100 mil hands. So the smaller is your sample the less chance for you will be to ruin.

bb means – Big Blinds and BB means Big Bets – standard abbreviation. Also HM2 has 2 different stats for std dev. One is bb per 100 hands and is as in examples. Another is just std dev. So the difference is like, eg, for midstack nlhe 65 vs 6.5. You may put in the description than you use std dev per 100 hands.

Also a qustsion: “Minimum bankroll for less than 5% risk of ruin” – does it mean that a player continues to play the same limit up to the end or that he goes down the limit at some point (eg, then he has the same amount of bb left for a lower limit)?

First off this is excellent and clean! I am starting a computer science minor next semester, although I’ve already begun to learn about c and java on my own, and was curious as to how you wrote this application. Like what language you used and what sort of things went into making this. I’d really appreciate any thing you could tell me.
Thanks

am a Mental Game Coach in the poker industry. I currently am sending my Mental Game Coaching clients over to this website to learn about the true effect of variance in their game. I believe if people used the simulator above and we’re more able to understand how much variance will affect their results, some issues of Tilt will be resolved.